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I have been searching for a lemma in ssreflect that represents sum linearity, so that I could transform

sum(a) + sum(b) = sum(c)

into

sum(a+b) =sum(c)

and then derive into

a+b = c.

Which could be suitable in this case?

The goal:

\big[Rplus/0]_(i <- fin_img (A:=U) (B:=R_eqType) X) (.  .  .) +
\big[Rplus/0]_(i <- fin_img (A:=U) (B:=R_eqType) X) (.  .  .) =
\sum_(u in U) X u * `p_ X u
Fusen
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1 Answers1

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I think you are looking for the big_split lemma. But it is hard to know without knowing what goal you're trying to prove in more detail...

Arthur Azevedo De Amorim
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  • Yes, this was the one. Thank you! – Fusen Apr 27 '21 at 14:30
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    In particular that last derivation looks a big strange, there are very few cases where `sum a = sum b -> a = b` – ejgallego Apr 27 '21 at 16:23
  • In practice when needing a lemma about bigops, it is often necessary to go and read the lemma statements in file bigop.v They are grouped according to the properties that are required of the binary operation. In this case, you need this operation to be both associative and commutative. – Yves Apr 27 '21 at 17:01